The Belgian midfielder said he was keen to experience success in the Champions League, but added that he could also fulfil his ambition at Chelsea.
Real became the first club to retain the European Cup in the modern era when they beat Juventus 4-1 in the Champions League final in Cardiff on 3 June.
The Spanish giants are expected to make a big-name signing in the summer transfer window to further strengthen a squad that won the La Liga title, the Champions League and the Club World Cup.
Chelsea will return to the Champions League next season after winning the Premier League title, with reports suggesting that manager Antonio Conte has been handed a £200m ($257m) transfer war chest to mount a successful campaign in Europe.
"Of course, I would consider it if Madrid made an offer," Hazard was quoted as saying by Sky Sports.
"I am keen to win trophies. It would be great to win the Champions League. But Chelsea's goal is to win the Champions League as well. Honestly, I do not know what will happen.
"I only know that I still have a contract with Chelsea for three seasons and that we just had an amazing 2016/17 campaign. We want to continue on this path and want to build on this in the Champions League.
"I am feeling very well at Chelsea. But you never know what will happen."
Hazard added that he had not spoken to Chelsea about extending his contract and that he was only concentrating on Belgium's upcoming World Cup qualifier against Estonia for the moment.
"I have not met with the board yet to discuss a new deal. I have two games with Belgium coming up first and I am off on my holiday after that. I want to think about football as little as possible," the 26-year-old said.